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Problem solving methods in combinatorics

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✦ Table of Contents

Cover
© 2013
Contents
Introduction
For the Student
1: First Concepts
1.1 Sets and First Countings
1.2 Induction
1.3 Paths in Boards
1.4 A Couple of Tricks
1.5 Problems
2: The Pigeonhole Principle
2.1 The Pigeonhole Principle
2.2 Ramsey Numbers
2.3 The Erdos-Szekeres Theorem
2.4 An Application in Number Theory
2.5 Problems
3: Invariants
3.1 Definition and First Examples
3.2 Colorings
3.3 Problems Involving Games
3.4 Problems
4: Graph Theory
4.1 Basic Concepts
4.2 Connectedness and Trees
4.3 Bipartite Graphs
4.4 Matchings
4.5 Problems
5: Functions
5.1 Functions in Combinatorics
5.2 Permutations
5.3 Counting Twice
5.4 The Erdos-Ko-Rado Theorem
5.5 Problems
6: Generating Functions
6.1 Basic Properties
6.2 Fibonacci Numbers
6.3 Catalan Numbers
6.4 The Derivative
6.5 Evaluating Generating Functions
6.6 Problems
7: Partitions
7.1 Partitions
7.2 Stirling Numbers of the First Kind
7.3 Stirling Numbers of the Second Kind
7.4 Problems
8: Hints for the Problems
8.1 Hints for Chap. 1
8.2 Hints for Chap. 2
8.3 Hints for Chap. 3
8.4 Hints for Chap. 4
8.5 Hints for Chap. 5
8.6 Hints for Chap. 6
8.7 Hints for Chap. 7
9: Solutions to the Problems
9.1 Solutions for Chap. 1
9.2 Solutions for Chap. 2
9.3 Solutions for Chap. 3
9.4 Solutions for Chap. 4
9.5 Solutions for Chap. 5
9.6 Solutions for Chap. 6
9.7 Solutions for Chap. 7
Notation
Further Reading
Index

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